"It's a big game. But not many people gave us much hope of turning up and putting Sri Lanka under pressure. We'll try to do the same on Sunday and hopefully get the two points," said Vaughan.
Set 236 to win against Sri Lanka, England finished on 233 for eight after 21-year-old all-rounder Ravi Bopara, in only his fifth match at this level, was bowled off the last ball by Dilhara Fernando needing just three to win.
Defeat was especially tough on Bopara, whose career-best 52 not out nearly guided England, who'd collapsed to 133 for six before his stand of 87 with wicket-keeper Paul Nixon (42), to an improbable win.
But defeat left England fifth in the standings on two points ahead of their return to the Sir Vivian Richards Stadium to take on table toppers Australia.
Sri Lanka, New Zealand and South Africa - the other teams widely tipped to make the semis - occupy the next three spots.
If England are to have a realistic chance of joining them, they need to beat either Australia here on Sunday or world number one South Africa in Barbados on April 17.
England held Sri Lanka to 235 all out, with fast bowler Sajid Mahmood taking a career-best four for 50.
But that was always likely to prove a tough target for a side with a faltering top three.
Vaughan was caught behind for nought as England slumped to 11 for two.
Then the unlucky run out of Ian Bell for 47, after bowler Sanath Jayasuriya deflected the ball onto the stumps, sparked a collapse that saw England lose four wickets for 32 runs as 101 for two quickly became 133 for six.
"We lost two early wickets but we were 101 for two with 25 overs left - that's a position you'd buy every game," said Vaughan.
"But we just didn't get a guy to that 80 or 100 which we keep talking about," he added of an innings where Kevin Pietersen, rated the world's leading one-day batsman, top scored with 58 before being caught and bowled by off-spinner Muttiah Muralitharan.
Vaughan hinted that opener Andrew Strauss, close to selection for this match, could come in after Ed Joyce made just 10.
"It was a difficult decision but we are going to discuss what we feel is the best formula going into the game on Sunday," said the captain.
Bopara, asked what his plan was when he came to the crease, said: "I had a quick chat with 'Nicko' about knocking it about for the next 10 or 15 overs and then seeing where we were at for the last five."
There was added tension when Fernando stopped in delivery as he prepared to bowl the final ball before re-starting his run and dismissing Bopara.
"I think he was just trying to see which way I'd go. But I can't stop him from stopping," said Bopara.
Vaughan admitted he thought the game was up when Bopara came in.
"It was looking a long shot to be honest," he said.
"The way Bopara played a gem of a flick over fine leg (for four in the last over off Fernando), I thought it was there. Full credit to Fernando. He held his nerve in the last two balls."